Novel ${\mathbb{Z}}_2$-topological metals and semimetals

Abstract

We report two theoretical discoveries for ${\mathbb{Z}}_2$-topological metals and semimetals. It is shown first that any dimensional ${\mathbb{Z}}_2$ Fermi surface is topologically equivalent to a Fermi point. Then the famous conventional no-go theorem, which was merely proven before for $\mathbb{Z}$ Fermi points in a periodic system without any discrete symmetry, is generalized to that the total topological charge is zero for all cases. Most remarkably, we find and prove an unconventional strong no-go theorem: all ${\mathbb{Z}}_2$ Fermi points have the same topological charge ${\nu }_{{\mathbb{Z}}_2}=1$ or $0$ for periodic systems. Moreover, we also establish all six topological types of ${\mathbb{Z}}_2$ models for realistic physical dimensions.

4 pages with Supplemental Material, 6 figures. Accepted by PRL

References in corpus (16)

• The electronic properties of graphene
• Classification of topological insulators and superconductors in three spatial dimensions
• Topological Field Theory of Time-Reversal Invariant Insulators
• Discovery of a Weyl Fermion Semimetal and Topological Fermi Arcs
• Theoretical Discovery/Prediction: Weyl Semimetal states in the TaAs material (TaAs, NbAs, NbP, TaP) class
• Weyl semimetal phase in non-centrosymmetric transition metal monophosphides
• Topological response in Weyl semimetals and the chiral anomaly
• Classification of stable three-dimensional Dirac semimetals with nontrivial topology
• Topological Defects and Gapless Modes in Insulators and Superconductors
• Topology of crystalline insulators and superconductors
• Classification of reflection symmetry protected topological semimetals and nodal superconductors
• Unexpected mass acquisition of Dirac fermions at the quantum phase transition of a topological insulator
• Topological zero modes and Dirac points protected by spatial symmetry and chiral symmetry
• Dirac semimetals $A_{3}Bi$ ($A$=Na,K,Rb) as $Z_2$ Weyl semimetals
• Surface Fermi arcs in $Z_2$ Weyl semimetals $A_{3}Bi$ (A=Na, K, Rb)
• Disordered Weyl semimetals and their topological family

Cited by in corpus (13)

• Unified theory of PT and CP invariant topological metals and nodal superconductors
• $PT$ Symmetric Real Dirac Fermions and Semimetals
• A Family Group of Two-dimensional Node-Line Semimetals
• Quantum simulation of exotic PT-invariant topological nodal loop bands with ultracold atoms in an optical lattice
• Superconductivity in doped inversion-symmetric Weyl semimetals
• Realizing and manipulating space-time inversion symmetric topological semimetal bands with superconducting quantum circuits
• Observation of gapped state in rare-earth monopnictide HoSb
• Dirac surface states, multiorbital dimerization and superconductivity in Nb- and Ta-based A15 compounds
• Generalized Fermion Doubling Theorems: Classification of 2D Nodal Systems in Terms of Wallpaper Groups
• Emulating topological currents arising from a dipolar parity anomaly in two-dimensional optical lattices
• Topological optical Raman superlattices
• Exotic Haldane Superfluid Phase of Soft-Core Bosons in Optical Lattices
• Predication of topological states in the allotropes of group-IV elements